The gallbladder stores bile, which is produced by the liver. The bile goes to the 2nd part of the duodenum (not the stomach, dem bones) via the bile duct, which usually passes through the head of the pancreas and enters the duodenum through the ampulla of Vater (sphincter of Oddi).
The gallbladder contracts and releases bile in response to CCK (cholecystokinin), released when fatty food (bile emulsifies fats making them easier to digest) is found in the stomach and duodenum.
Infection of the gallbladder is known as cholecystitis. Cholelithiasis is gallstones in the gallbladder. Gallstones going into the bile duct is choledocolithiasis.